The `x-` component of a certain vector in `x-y` plane is 2 units and `y-` component is `+2sqrt(3)` units. What is the magnitude of the vector.

Explanation

To find the magnitude of the vector given its components in the x-y plane, we can follow these steps:

### Step 1: Identify the components of the vector
The x-component of the vector \( a_x \) is given as 2 units, and the y-component \( a_y \) is given as \( 2\sqrt{3} \) units.

### Step 2: Use the formula for the magnitude of a vector
The magnitude \( |A| \) of a vector \( A \) with components \( a_x \) and \( a_y \) is calculated using the formula:
\[ |A| = \sqrt{a_x^2 + a_y^2} \]

### Step 3: Substitute the values into the formula
Substituting the values of \( a_x \) and \( a_y \):
\[ |A| = \sqrt{(2)^2 + (2\sqrt{3})^2} \]

### Step 4: Calculate \( a_x^2 \) and \( a_y^2 \)
Calculating \( a_x^2 \):
\[ (2)^2 = 4 \]
Calculating \( a_y^2 \):
\[ (2\sqrt{3})^2 = 2^2 \cdot (\sqrt{3})^2 = 4 \cdot 3 = 12 \]

### Step 5: Add the squares of the components
Now, add the results:
\[ |A| = \sqrt{4 + 12} \]

### Step 6: Simplify the expression
\[ |A| = \sqrt{16} \]

### Step 7: Calculate the final magnitude
Taking the square root:
\[ |A| = 4 \text{ units} \]

Thus, the magnitude of the vector is **4 units**.

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